<h2>Problem 78</h2>
<div style="color:#666;font-size:80%;">10 September 2004</div><br />
<div class="problem_content">
<p>Let p(<i>n</i>) represent the number of different ways in which <i>n</i> coins can be separated into piles. For example, five coins can separated into piles in exactly seven different ways, so p(5)=7.</p>
<div style='text-align:center;'>
<table cellspacing='0' cellpadding='10'>
<tr>
<td>OOOOO</td>
</tr>
<tr>
<td>OOOO&nbsp; &nbsp;O</td>
</tr>
<tr>
<td>OOO&nbsp; &nbsp;OO</td>
</tr>
<tr>
<td>OOO&nbsp; &nbsp;O&nbsp; &nbsp;O</td>
</tr>
<tr>
<td>OO&nbsp; &nbsp;OO&nbsp; &nbsp;O</td>
</tr>
<tr>
<td>OO&nbsp; &nbsp;O&nbsp; &nbsp;O&nbsp; &nbsp;O</td>
</tr>
<tr>
<td>O&nbsp; &nbsp;O&nbsp; &nbsp;O&nbsp; &nbsp;O&nbsp; &nbsp;O</td>
</tr>
</table>
</div>
<p>Find the least value of <i>n</i> for which p(<i>n</i>) is divisible by one million.</p>

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